Because their cores are not perfectly circular or because of stress, inherent to the structure or externally applied, practical single mode fibers are birefringent. These sources of birefringence are reviewed briefly. A simple model for the fiber consists of a combination of one linearly birefringent element and one circularly birefringent element. Depending on the magnitude of the birefringence, different techniques of evaluating the parameters of the model may be suitable. Several methods appropriate for low and high birefringence fiber are described and some of their advantages and disadvantages outlined. In an idealized single mode optical fiber, in which none of the structural or optical parameters varies with the azimuthal coordinate, all polarization states within the fundamental mode are degenerate; that is, neither the phase nor group velocity depends on polarization. In practice, however, this degeneracy is usually lifted by non-circularity of the core, by inherent stress in the guiding structure, or by stress resulting from bending, pressure, or twisting. Light entering the fiber with an arbitrary polarization state will then be resolved into a pair of orthogonal polarization states that propagate with different velocities. As a phase shift develops between them, the state of polarization will vary periodically along the fiber. The orthogonal states may be linear, circular, or in general elliptical, depending on the specific mechanisms involved.